The Food Inflation Puzzle

I was hoping the food inflation roller coaster was behind us as Covid faded, but tariffs, if left in place long enough, will push food prices higher. As such, I thought it was a good time to understand the food supply chain and the corresponding drivers of food inflation.

We start where many supply chains start, oil and energy. Oil is the first big rock in the food supply chain and it strongly influences the cost of Farm Products. Farm Products influence the cost of Food Manufacture, which in turn influences Grocery Retailer's cost of goods. Then we layer on the Grocery Retailer's markup or gross margin which takes us to the register and the price we pay for groceries. The government tracks cost data along this path.

• West Texas Intermediate oil prices

• Producer Price Index for Farm Products

• Producer Price Index for Food Manufacture

• Producer Price Index for Grocery Retail

• Consumer Price Index for Food-at-Home (what we pay at the register)

Time Lags

If we are going to model the supply chain, the first thing to figure out is how fast or slow costs move along this path from oil to the grocery register. This is done by lagging the data. For example, if we have CPI Food-at-Home and PPI Food Manufacture, we shift down the manufacture costs one month at a time until the two lines align. An example is below. It shows the time series data for Food Manufacture and the CPI Food-at-Home. We can see they are just off and if we shifted the red line down a few periods it would align better. We find the lag by looking at the correlation between the target variable CPI Food-at-Home with multiple PPI Food Manufacture lags. The lag with the highest correlation is likely the optimal choice.

The chart below tells us the number of optimal lags between PPI Food Manufacture and CPI Food-at-Home. Looking at the green line, we hit the highest level at four months. That is where the correlation is the highest so that is the optimal lag for these two variables. In other words, food manufacture cost changes take about four months to reach grocery prices.

There are two interesting things to note in the chart above. First the height of the line and the second is the maximum value of the line. The higher the line, the more correlated it is with the price of groceries. We can see that that most influential element in the supply chain with grocery prices is PPI Food Manufacture, and as mentioned above, it peaks at four months. We can also see that the PPI Farm Products is the second highest and peaks at about 7 months. Oil peaks at about 9 months which makes sense. The farther back in the supply chain, the longer the lag and the longer it takes to impact grocery prices. It is interesting to note that PPI Grocery has no lag which is expected because the retail markup is immediate. I also included retail wages to see if there was anything interesting, but nothing really stands out.

Build the Model

With an understanding of the lags we can begin to assemble the model. The model is trying to explain the variation in CPI Food-at-Home YOY by using the patterns in oil and the various PPIs. The model's objective is to understand what food inflation might look like in six months. We pick six months because of the lag structure. Since the lags are 5-7 months, we can use these forward looking PPI measures to create a descent food inflation estimate.

In building the model, we find the biggest drivers of CPI Food-at-Home are PPI Food Manufacture and PPI Grocery. These have the most impact because of their proximity in the supply chain. The chart below is the actual vs the forecasted values, so we can see that we are a bit under in 2020-2023, which is not ideal but expected because the variations in CPI Food-at-Home were extreme. Overall, the model is tracking pretty good with the actual values and is explaining about 80% of the ups and downs in the data.

Validate the Model

The next step is to validate the model. The model may fit the data well but how will it perform when we holdout data and rerun the model. We purposely remove part of the actual data from the forecast and then rerun the forecast. This allows us to compare our forecasted values with actual data that was not included in the model. This gives us a sense of how the model will perform when we forecasting forward. 

We did this by holding out 24 months of data and then forecasting a rolling six month forecast and comparing it to the actual values. We can see that when inflation was higher in 2023 the error was larger. For example, in Feb 2023, food inflation was 8.3% and we were off by about 1.75 percentage points. Not great but not bad if one remembers the uncertainty around food inflation in 2022 and 2023. But we do see the model's accuracy improving significantly as Covid and the myraid of market distortions fades. For much of 2024 the model has been off by less then 0.5 percentage points. 

Forecast Forward

With a solid understanding of the lag structure and the low errors in the validation results, we can forecast the next six months with some confidence. The blue line is the actual CPI Food-at-Home values. The red line is the forecast, and the grey area is the confidence intervals.

The model is telling us that CPI Food-at-Home inflation is expected to go up over the next six months. The CPI Food-at-Home started to climb in the fall just after the election - October 1.1%, November 1.6%, December 1.7%, and January 2025 1.9%. The model shows this trend continuing, hitting 3.2% YOY by July 2025. Overall, a 3.2% CPI Food-at-Home increase is not too significant and can help grocery retailers in the short run if units do not decline by more, but shoppers have run out of stimulus savings and many are fed up with higher prices so it will be interesting to track units. 

So how does this CPI Food-at-Home forecast impact the Grocery Sales forecast? CPI Food-at-Home is the biggest driver of grocery sales so some inflation is good, but higher prices can also dampen units. I will be updating my Grocery Forecast next week. I had to take some time off to see what was happening with tariffs. Not sure I am any more clear today, than last month, but we will insert this CPI Food-at-Home forecast into the Grocery Sales forecast next week.